TL;DR
This paper provides a combinatorial interpretation of a generalized formula related to rational Catalan numbers, connecting it to Springer fibers, binary necklaces, and anchored Dyck paths.
Contribution
It offers a new combinatorial interpretation of a formula generalizing rational Catalan numbers, linking Springer fibers with binary necklaces and anchored Dyck paths.
Findings
Established a combinatorial interpretation involving binary necklaces and anchored Dyck paths.
Connected the formula to the study of Springer fibers.
Extended understanding of rational Catalan number generalizations.
Abstract
We answer a question of Simental by providing a combinatorial interpretation of a formula which generalizes rational Catalan numbers and which appears in the study of Springer fibers. We provide an interpretation in terms of binary necklaces as well as anchored Dyck paths.
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